precalculus

[dire ginkgo]

WE GOT THIS!!!

[mystic sluice]

did you not get any practice assessments on ap classroom?

GL everyone

bruh my teacher sent the practice the night before the exam

[dire ginkgo]

😔

I have the unit circle in my head, mastered frq 3 very familiar with the other 3 frqs, my only flaw is polar and rectangular equations

What y’all think I would get

[mystic sluice]

5

if not 4

ig if you are strong on everything else you should get a 5

polar is less than 1/3 of the exam anyways

[dire ginkgo]

Id be fine with a 4 but I need that 5, I’m very cooked for physics I need a tutor

Ap physics 1

Test is this Friday and I’m screwed

[viscid thistle]

Hey guys, anyone online?

I'm doing a practice sheet for calculas, indefinite integration. If anyone interested in solving with me, dm me

[wary agate]

I got one question for the ap test tmmr

,rcc

,rccw

[wary agate]

Nice

Ok but basically this question it’s obvious that f does not have an inverse

But when I go to explain it I can’t only say it doesn’t pass the horizontal line test

What can I say to get the frq point

[winter comet]

state that its not one-to-one and give an example proving that its not one-to-one based on the table

[wary agate]

So just give two points pretty much

[winter comet]

which I can't see but I assume has a contradiction

[wary agate]

Ok

[warm cove]

AP exam is over, did a lot of studying yesterday and I think it paid off as I have confidence I did a good job, the questions were really easy compared to the ones my teacher gave out so I was better prepared

[dire ginkgo]

I didn’t get this question

I just finished

No way I didn’t get a 5

[mystic sluice]

did anyone remember getting 400pi for one answer

[marsh cipher]

how do i start on this? im hella lost lol

[glass solar]

i dont know but i think The area of the rectangle is the product of its width and height

the windth of the rectanle is x from the lower right corner to the vertical line at x)

the high of the triangle is f(x) x to the power of fourth

the function is A(x)=xx(to the power of fourth)=xto the power of fifth

o maximize 𝐴 ( x ) = 𝑥 5 A(x)=x 5 , you would use graphing tools or a calculator to analyze the behavior of the function over the given interval [ 0 , 6 ] [0,6].

[marsh cipher]

answer is 6x^4-x^5 then use desmos to find maximum area, it was x(6x^3+x^4)

i think ill just ask professor tomorrow to elaborate it

[uncut mantle]

yes

bro the min max quadratic question was so dumb

i didnt realize that you could just say that the max was the end of the domain

[mystic sluice]

Broo fr

I said something dumb

I thought they ignored the domain on that question

I thought the max was somewhere in between the domain

[mystic sluice]

Do you remember what you put for c and d

[uncut mantle]

1/800 should be c I think but it can vary

D is 0

[zinc herald]

How do you determine rational points of an elipse on a graphing calc

I have hw that says "graph the relations on a graphing calc and identify 4 additional points on the graph whose coordinates are rational"

and then gave 25x^2+9y^2=255

[long tapir]

Im a bit confused as to how to find the answer to this problem

Mainly because of the square root

[willow skiff]

have you tried converting it to x^2 / a^2 + y^2 / b^2 = c^2 ?

[zinc herald]

yes

[willow skiff]

you can divide top and bottom by x^5

[zinc herald]

just to make it easier

let X=5x and Y=3y

so you get X^2 + Y^2 = 255

and now it's just a circle

and I can divide by 255

but IDK what to do

it's not 225

it 255

15^2=225

[willow skiff]

oh right

[zinc herald]

I am leaning on that their is no solution

[willow skiff]

yeah it doesn't seem possible

ask your teacher then

[zinc herald]

sure

also, when I rechecked the hw

it said to skip this specific question

so I think the textbook might have made an error

[willow skiff]

I bet they meant 225 and not 255

[zinc herald]

yeah

[willow skiff]

alr cool

[zinc herald]

but now I kinda want to prove that their is no solution

but apparently that requires like Diophantine stuff

😭

[willow skiff]

https://www.quora.com/How-do-you-prove-that-x-2-y-2-21-has-no-solution-in-rational-numbers

[willow skiff]

I mean it is a Diophantine equation after all

but it's not too bad once you know the technique

255 is divisible by 3 which makes a lot of sense considering squares modulo 3

[zinc herald]

thanks

[zinc herald]

I will look into it

[solid shuttle]

This one has no rational solutions

[cedar idol]

Hey, I'm struggling with this one calculus & vectors (high school) problem, is anybody able to help me out with it? I don't know what I am doing wrong. My work is attached to this text, Thank you.

"A pilot in an airplane with an airspeed of 1000km/h wishes to fly to a city 2000km due east. There is a wind blowing from 025 degrees at a speed of 100km/h.

In what heading should the pilot steer?"

[solid shuttle]

Resulting speed is a sum of 2 vectors of length 1000 and 100. The direction of a 100-vector is known. You have to find the direction of the 1000 vector such that their sum pointed exactly eastward. So, it is a resulting vector that should point East, not the 1000 one.

[empty otter]

are 3d vectors in precalc or not

[viral junco]

What did you get for this in the end?

[willow skiff]

usually not

depending on curriculum they can be

[spice perch]

They are

[viscid thistle]

divide it by x^5

[brisk glen]

<@&268886789983436800> This should be the final one

[zinc herald]

limits are in ur precalc?

[long tapir]

Yep

[open dawn]

someone teach me calculus and get $0

[zinc herald]

lmao

watch 3b1b

• khan acedemy if you want problems

[zinc herald]

IDK if you still need help one this @long tapir , but after you divide by x^5, be careful about the sign

[long tapir]

Alr i got it i believe

Thank you!

[zinc herald]

np

[vale spindle]

do you guys watch youtube video courses on precalc? is it good enough on its own to self study?

[willow skiff]

you need to get some practice in too

Khan Academy is a decent source of practice

but textbooks will have more in-depth questions

[elfin niche]

I am doing piecewise, I sorta understand how to do the x portion of the graph but not the y portion, do I just swap the x with a y?

[uncut mulch]

no, you shouldn't be swapping x with y

you sub the value you chose for x into x (for that piece)

and the way you're setting up the tables implies you aren't using the proper x values

where's 4 and 9 coming from in the second table?

[elfin niche]

The 4 and 9 come from the 2x-4 I substituted the x with numbers to get those two

[uncut mulch]

what numbers were you substituting with?

[elfin niche]

I am unable to give you a concrete answer since I did the math in my head but I think for the first it was replacing the x with 8.

[uncut mulch]

2 * 8 - 4 would be 12 though

but regardless

you should have labels on your columns

with values of x you're using in the left column

and the respective f(x) value in the right column

f(x) = -x-4 for x<=0

__________
-5   | 1
-4   | 0
-3   |
-2   |
-1   |
0    |```

and similar idea for the other piece

if you want to make a table of values to get your points

[elfin niche]

I think I get it, so I plug in a number that matches the piece, and what that number equals when plugged in is the y value

[uncut mulch]

yes

[elfin niche]

hooray thank you

[hushed sphinx]

Uh, those two f(x) values should be 1 and 0 rather than -9 and -8, surely.

[uncut mulch]

lol shit.

was half awake

[elfin niche]

Am I supposed to multiply the number by 3 since it is greater than zero for the last piece?

Also where did I go wrong with number one?

[vale spindle]

dosen't -x-4 tell you the y intercept is on minus 4?

and -x is -1/1 or 1/-1 i think

so you would move indefinetly 1 y 1 x and depending on the direction the y or the x would be the negative one

[prisma aurora]

guys im new here but i have a quick question to those already in pre cal

rn im in alg 2 and ima take pre cal over the summer thru UTHS any tips or some ? bc ngl im not that good at math but i needa get ahead i lwk slacked alot in alg 2

[lethal sand]

precalc is like basically a repeat of alg 2

[distant oasis]

Can someone else I’m not sure how I would graph

I’m very lost

[inner viper]

I have an idea

For first one, imagine point -3 and then point it anywhere

And then make an arrow to it until your graph ends to -∞

Do these for others too

Since we don't know what's infinity, you need to show that it's going forever

With a ray

[coarse thorn]

??

Step 1: draw the given asymptotes
Step 2: follow the limits given in the question

[distant oasis]

Would I need to put points to where I put it

Like close or open dots

For the x=1 and y=-3

[coarse thorn]

Open dot is for points where function is undefined

No need for it here

Open desmos

(-3x+1)/(x-1)

Could be the fn

[coarse thorn]

No

@distant oasis

[mild inlet]

Do you guys know if a logarithm can be written with just arithmetic math in 1 mathematical formula

It sounds impossible but surely it's possible if floor division and absolute values are allowed

because I was told by AI that it's not possible since a logarithm requires conditions (if/else) but surely that can be simulated with floor division and absolute values

[safe basin]

Well what operations are you allowing for

[mild inlet]

I wrote a help thread https://discord.com/channels/268882317391429632/1373811303038189628

Basically I'm allowed only floor division, which u can use to simulate the absolute value

But in general, no if statements, no for loops, no special functions or classes, no domain and range restrictions, nothing

just floor division, normal division, and the other remaining arithmetic operations

if anyone has a solution to this (even tho it sounds impossible) pls let me know ill pay u $10

[safe basin]

LMAO you shouldn’t offer money it’s against the server rules

but you’ll probably find someone to help here anyways

[mild inlet]

oh ok, but ill send money off server but its been a popular challenge in my community

[hushed sphinx]

With those tools, it sounds like you can only make functions whose growth matches a rational function, which logarithms don't.

[mild inlet]

wdym? can u explain?

but cant you simulate if and else conditions using floor division?

i swear u can

[hushed sphinx]

I'm not sure exactly what "floor division" is, but assume it is division with the quotient truncated to an integer.

[mild inlet]

ya

thats what i mean sorry, floor division that truncates to an integer

so within my environment i can use decimals and integers, and normal division and truncated division

[hushed sphinx]

It won't help you with the argument I have in mind, because even if you can build if-then-else, you can only have finitely many cases anyway.

[mild inlet]

But to be honest I only need a working if-else statement to do this

because i already have a previous version of a logarithm using only arithmetic calculations that also uses if else statements using step wise reduction, if i can normalize the if statements to just arithmetic math with the truncated division it can be possible

[hushed sphinx]

If you only need your logarithm function to work for a bounded range of inputs, you can hope for an approximation that works well there.

[mild inlet]

ok sure this is good enough, I can allow only integers I guess

decimals will be too complicated, so whole numbers is fine and no zero since i think logs dont allow zero

[hushed sphinx]

Unfortunately the integers are not a bounded range ...

[mild inlet]

hmmmm

like A - B?

ok i can do 1 - 999 i guess

or like 1 - the integer bit overflow square root or something idk lol

log i mean

can someone help me i have lots of money ill pay u $50 if anyone has a solution to this

[hushed sphinx]

Well, if you have an upper bound for the input and you're satisfied with an approximate output, then there are no theoretical obstacles -- thanks to the Weierstrass approxiation theorem, you can approximate the logarithm arbitrarily well by polynomials of sufficiently high degree.

[mild inlet]

yooooo

yeah I was thinking polynomials

wait

ok yeah polynomials

[mild inlet]

can u help me? you probably have an solution in mind

[hushed sphinx]

I won't be able to tell you which polynomial, unfortunately.

These were only strictly theoretical musings.

[mild inlet]

bro what does that mean

can someone help me if you have a solution https://discord.com/channels/268882317391429632/1373811303038189628

[mild inlet]

yooo thanks bro ai said its brilliant

[chrome ether]

!nogpt

[tender quest]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[muted moth]

@mild inlet as mentioned all of the way at the beginning of the thread, we need to know the range of values you expect to be fed into this function in order to give you anything reasonable. But if you can give me a minimum value, a maximum value, and a maximum tolerance, I can give you back a polynomial or rational function that will give you your result.

Alternatively, if you wish to do it yourself, the procedure I was going to use is known as the Remez algorithm

[mild inlet]

sorry

[mild inlet]

sure no problem

minimum values for values B and X are 1, it cant accept any values that give an error

so log1_1 should be whatever the standard logarithm function gives

[muted moth]

Ignore the base

You can use change of base formula

What are the allowed values of x?

[mild inlet]

ohhhh thats so smart true

[mild inlet]

how do I figure out?

[muted moth]

You figure out what values are likely to go into the function, and which values you do not care about

Or alternatively, you have to come up with a method of mapping larger values into the smaller range via a continuation somehow

Like ln(xy) = ln(x) + ln(y) in your case, if you have access to both ln(x) and ln(y) then you can figure out ln(xy)

For instance, if you decide you want to implement log_2, for inputs between 1 and 2, then if you're given x = 6.3 you would need to divide by 4 to get x into the proper range. Fortunately, for floating point numbers, you have the exponent, and if you can extract it you know how much you need to divide or multiply your input by

Oh, I should take this into the thread

[viscid thistle]

Hi, is there anyone who speaks spanish?

[hushed sphinx]

No, the Spanish language is a hoax; nobody actually speaks it.

[fiery crest]

I'm really really behind in trig and I have a midterm Friday. I've tried to watch the videos my instructor gave but I don't understand what he's doing and it's taking hours to solve one question at a time. Idk what to do anymore

[zealous bronze]

I can help

[pseudo zealot]

what do u need help on

[mild inlet]

cookiezi

[alpine shore]

@fiery crest Can I help you please?

[bleak forge]

#odes-and-pdes help pls

[viscid thistle]

So there's 2 questions I got wrong on my final for pre cal

The first was prove
secx-1/tanx = secx+/tanx

It's probably easy but verifying solutions stump me

And fins sin2x if tanx is 24/7 cos>0

[viscid thistle]

For the second I tried getting secant but ended up with √527/7 and got scared by the square root and it freaked me out

[zenith elbow]

Can anyone help me? I have to do a 10-minute oral in maths and I'm doing it on Gabriel's horn , but it's too short.

[hushed sphinx]

That sounds like a difficult topic to do justice to without calculus.

[tawdry ibex]

hi
peles help me
I have a problem. I'm trying to solve time flexibility with math. We have a vision of a series of numbers that are repeating or a series of decimal numbers that are not divisible by anything at all.
p= 2X *9m =- 11
11 -= 0m + mp2 - 29 = 2.7580088765936458
OM = 0 -9 *1.2 + 0.4
mp = 8 + 7 * 78 - 3
and
x =?
m == X-2 * 82 ms

[hushed sphinx]

Please don't crosspost the same question between all the pre-university channels. I cannot follow exactly what you're saying, but it looks like responses should probably be in #prealg-and-algebra.

[slate fox]

can someone please help me with this

[sterile pulsar]

yeah sure

so you wanna ask something specific? Or the whole problem set?

[polar laurel]

Chatgpt is so bad at ts

[brazen sedge]

Can someone explain to me what a log is 🙏

(What(is(a(log(x)))))

Hope I did that right

[brazen sedge]

I don’t get the fancy wording 😔

Actually nvm

Just googled it

I understand it now

[safe basin]

[brazen sedge]

❤️ ❤️ ❤️

[willow bear]

no you didn't

[meager stump]

logarithm

I don't remember the definition but I think inverse of a power? (not as in negative exponent)

[granite wolf]

<@&286206848099549185> should I just differentitate both sides?

[hoary iris]

It might be calculus itself

#calculus

[granite wolf]

bhai iit ka sawal hai

sameer bansal

[hoary iris]

english! @granite wolf

[granite wolf]

you from India right?

[hoary iris]

yes but from south(idk hindi)

[granite wolf]

ohh my bad

it's from a book called sameer bansal

@hoary iris did you gave mains?

or are you a 26 tard?

[hoary iris]

no preparing for it

[hoary iris]

tard? that JEE channel?

[granite wolf]

nvm

[granite wolf]

you in class 12th ?

[granite wolf]

nvm

[hoary iris]

yes!

btw who are you? and how do you know about me? @granite wolf

[granite wolf]

its a long story

i had a chat with you

a few months ago

[hoary iris]

that same clone?

[granite wolf]

along with a couple of other dudes

[granite wolf]

yeah

[hoary iris]

wht happen to your pfp?

[granite wolf]

its a long story

[hoary iris]

now what happened clone?

[granite wolf]

im clone 😭

[hoary iris]

yes i trust you

what made you cam here?

[dusty jay]

You integrate and find g(x) and differentiate ✌️👍

[elfin niche]

I don’t understand how to pick the points for the piece wise

[willow bear]

ok let's just crop away the black bands that are like 3 times as tall as the image itself

[willow bear]

there's no sacred rule that you always have to follow, but generally the points you want to pick always are the ones where the cases switch over

in your case that's x=1

so pick that and some other easy values around that

[violet stratus]

hi

can you explain fx a bit

[elfin niche]

So like for example, for the top one I should pick values that are less than 2 and maybe also include 2?

[willow bear]

you should include 2 itself yes

and also something to the left of 2 and something to the right of 2

[violet stratus]

can anyone explain fx a bit

[elfin niche]

Hi, do you mean f(x)?

[violet stratus]

yes

i am new

[elfin niche]

Okay! , so f(x) is just the y-value, kinda like how Bruce Wayne is Batman

[violet stratus]

okay

i am new to the concept

btw which grades r included in precalculus

[elfin niche]

well for me precalculus is a senior and junior high school class and they also teach it in some colleges

[violet stratus]

okay

that means i am in the wrong group

which group is for 8th graders

[elfin niche]

hmm, I think that the help-forum can help you

[violet stratus]

okay thanks

sorry for causing any trouble

[elfin niche]

you didn’t do anything wrong

[violet stratus]

is it still okay if i join this group

i just really like math

[elfin niche]

yeah man it’s whatever

[violet stratus]

thanks

[high pelican]

You’re in the right discord then

[elfin niche]

I’m getting a bit doomer about math again

[hoary iris]

Is $\lim_{x \rightarrow 0}(log_{a}x) = -\infty \ \forall \text{a}\in(0, \infty)$?

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

why not? @willow bear

,w lim_{x->0} log_{a}(x)

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by kingdanger6266

[hoary iris]

what does this mean then?

[willow bear]

it depends on whether a < 1 or a > 1

if a > 1 then the limit is -∞ but if a < 1 then it's +∞

[hoary iris]

oh understood! thank you

[merry widget]

isnt it supposed to be the other way around

[willow bear]

he was asking for the limit as x goes to 0 so no it is the right way around

[crisp thicket]

sup

i like math

[high pelican]

Yo

[polar laurel]

@wooden nymph HI BRO

[wooden nymph]

hibrother

[zinc herald]

can the parabola be considered a special case of the hyperbola just like the circle is considered the special case of an ellipse?

[river drift]

as conic sections they are distinct, the parabola is the case in between the ellipse and the hyperbola

[prisma aurora]

can someone help me with some pre cal

i genuily dont understabd the algrba behdin it

𝑏(𝑥) = 1 /𝑥+3 on [1, 1 + ℎ] - how to find the avg rate of change, ion get the algebra behidn it

or Let 𝑓(𝑥) = 1
𝑥. Find a number 𝑐 such that the average rate of change of the function 𝑓(𝑥) on the interval
(1, 𝑐) is − 1/4.

[willow bear]

do you mean $b(x)=\frac{1}{x}+3$ or $b(x)=\frac{1}{x+3}$?

[obsidian monolith]

Ann

[prisma aurora]

second option the bot provided

[willow bear]

it was me invoking the bot not the bot itself :P

anyway

...what exactly is unclear to you?

do you get lost in the sauce when simplifying?

or do you get confused even at the initial setup

like...

the average rate of change of $f(x)$ on $[a,b]$ is by definition the quantity $\frac{f(b)-f(a)}{b-a}$ --- there isn't any special process to ``finding'' this aside from plug-and-chug.

[obsidian monolith]

Ann

[violet stratus]

,w what is a histogram

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by cr7xhaaland._91903

[modest bolt]

So it provides definitions too, didn't know that

[echo sinew]

,w Italy

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by zuanon.alberto

[echo sinew]

And not only math lol

[violet stratus]

,w pakistan

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by cr7xhaaland._91903

[violet stratus]

yep

double checked

[prisma aurora]

the simplifying the set up is easy

[violet stratus]

we need a discussion sub-group to test these bot functions

[willow bear]

#bots

[willow bear]

sorry, i am not sure i understand you correctly

do you mean: "the simplifying is easy; the setup is where i'm lost"?

[prisma aurora]

sorry i was a little distracted

i meant to say the simplifying and acc doing the algebra for it challenges me

the set up is rather easy

[willow bear]

ok right

so you're gonna need to deal with fractions no matter what kinda by design, but if the formula for f(x) itself includes fractions then you may also need to deal with nested/skyscraper fractions

so if that is the case there's a trick you can do to make your own life somewhat easier

one moment

you still need to know how to work with fractions i.e. adding, subtracting, multiplying, maybe dividing fractions but this way is a bit easier @prisma aurora

[alpine shore]

Hello,I need help.

[prisma aurora]

i’m sorry i’m still a little lost

[heavy pewter]

use a³-b³ 🤔

[hidden birch]

what does this expand to

[willow bear]

do you understand what's written on the paper

[modest bolt]

Let 8+h=x³ → h=x³-8

[hidden birch]

nvm. got it

[willow skiff]

alternatively, use the definition of the derivative:

$$\lim_{x \to a} \frac{f(x) - f(a)}{x - a} = f'(a)$$

where $f(x) = x^{1/3}$, $x = 8 + h$, and $a = 8$

[obsidian monolith]

south

[prisma aurora]

yes up to the last part, is that the solution ?

[willow bear]

no not yet

i was gonna ask you now:

do you see how to simplify $\frac{1}{h}\paren{\frac{1}{4+h}-\frac{1}{4}}$?

[obsidian monolith]

Ann

[willow bear]

i can walk you through it if you need.

[prisma aurora]

no i still dont, im really weak on this stuff, ima give a guess though

acc not a clue distrucbe or LCD?

[hushed sphinx]

You could start by putting the two fractions being subtracted on a common denominator.

(This turns out to lead to progress, but it's such a natural thing to try that you should try it even if you cannot yet see whether it will make progress or not).

[willow bear]

the spelling on that "distrucbe" 💔

[willow bear]

very strongly seconding this

[prisma aurora]

small phone 😔

[willow bear]

anyway yes gonna reiterate

when you see two fractions being added or subtracted a natural first step to simplification is often to combine them into one

[prisma aurora]

i see and say if it was with a variable as one the denominators, can i just multiply the two denominators to get a LCD

In this case (4)(4+h)

[willow bear]

yes

though you should be on the lookout for common factors generally to get the lowest common denom

but in this case yes it's just the product

[vagrant nymph]

when in a question they say which of the following limits vanishes they mean which of the following limits is 0 right?

[prisma aurora]

okay thanks then we distribute the 1/h ?

i just wanted to say i really appreciate the help

[willow bear]

we don't distribute it no

[willow bear]

"vanish" means "become 0" yes

[vagrant nymph]

okay thanks

[willow bear]

no, we multiply 1/h by the simplified fraction from the bracket

[prisma aurora]

sorry that’s what i meant shoudl have been more clear

[willow bear]

yes you should've

"distribute" has a pretty specific meaning that should not be confused

[prisma aurora]

mb

[vagrant nymph]

in this question how do i comment about option a and b

[zinc herald]

what is the limit of f(x) as x-> infinity

@vagrant nymph

[vagrant nymph]

(a/b)^inf

[zinc herald]

yes

now what happens if a<b

say a is 1 and b is 2

[vagrant nymph]

waiy mb i had doubtf in opt a and c

if a<b limit is 0

i am not sure about a and c

[zinc herald]

well does A make sense

if a>b ?

[vagrant nymph]

if a>b than limit is infity

so does that imply limit does not exist?

[zinc herald]

I am assuming that

[vagrant nymph]

thats where i am confused in

[zinc herald]

typically, if it goes to infinity then it does not exist

it's not any real value

[vagrant nymph]

alr thanksss i did not know that

it matches with the answe tho

[zinc herald]

what

[vagrant nymph]

i did not know this

i got it now

thanks @zinc herald

[zinc herald]

np

[exotic barn]

hey@dry verge, I hope you don't mind me sharing a solution

from the previous question

[dry verge]

Thanks, I think I kind of understand it more. Sorry, sometimes I get overwhelmed and I need to recover from that in order to get things more.

[exotic barn]

It's okay!

[exotic barn]

5BC=AB*

[vagrant nymph]

is my soln correct?

[willow skiff]

right idea but that limit is still indeterminate

instead you should factor, so $\lim_{x \to 0} \frac{1}{x} \left(1 - \frac{x}{\tan x} \right) = \lim_{x \to 0} \frac{1}{x} \cdot (1 - 1)$

[obsidian monolith]

south

[vagrant nymph]

hmm okay leeme try again

[willow skiff]

you've written it in the form infinity - infinity, that's what I mean

[vagrant nymph]

but even in this you get 0/0 form only right?

[vagrant nymph]

yea thats why i was not sure🥲

[willow skiff]

it's a 0/0 form but the limit still exists

$\frac{0}{x} = 0$ except for $x = 0$ sure

[obsidian monolith]

south

[willow skiff]

so that would be a removable discontinuity at x = 0

[willow skiff]

wait sorry, your work does make sense

I'm just saying what you can't do is split apart the limits

$\lim_{x \to 0} \frac{1}{x} - \lim_{x \to 0} \frac{1}{x}$: no!

[obsidian monolith]

south

[vagrant nymph]

okay fair

got it

thankss

[willow skiff]

np!

[lament crag]

im taking AP precalculus ima need alot of help this school year coming

[willow skiff]

Always welcome on this server

[neon crag]

ditto the above

[woven meteor]

how did u guys leanr pre calculus?

[willow skiff]

school

[true geode]

"How do you keep your pants on during your stage performances?"
"...... belt"

[willow skiff]

what?

[true geode]

Vine reference

[willow skiff]

bruh.

[true geode]

https://youtu.be/F-xR-zA0GSI

(what it's a fokken goldmine of the Internet)

[lean drum]

I self studied

[vagrant nymph]

how do i learn the expansions in limits

its like all of them are the same😭

[modest bolt]

Learn the pattern they aren't same

Instead of learning e^x=1+x+x²/2!+x³/3!...
Try to learn e^x=x^0/0! + x^1/1! + x^2/2! + x^3/3! ...

I think it's easy this way to remember

[vagrant nymph]

hmm yea ig that workss

also what am i doing wrong in this question

[modest bolt]

The question's wrong

Your answer seems right

[winter comet]

?

you crossed out -1/24 and sin^2(x)/(24 x^4)?

[vagrant nymph]

sin^2x/x^2=1

so that becomes 1/24x^2

[winter comet]

lim x->0 sin^2(x)/x^2 = 1 but you can't evaluate just parts of the limit seperately

thats why you got an indeterminate form in the first place

[vagrant nymph]

or am i trippin

[vagrant nymph]

wait what

i have been doing taht

[winter comet]

[vagrant nymph]

hmm fair fair

than what do i do

[winter comet]

ig you could try expanding the sine terms 💀

[modest bolt]

Ok so got have 1)6

*gave 1/6

[vagrant nymph]

wont that be very tedious

[winter comet]

yeah

[modest bolt]

Bro's right here

[vagrant nymph]

umm okay ill try that

[modest bolt]

Limit are tedious

[winter comet]

i would probably just expand cos(sin(x)) as a maclaurin series and cos(x) as well tho ngl 💀

which would require going back to the top butuh

[modest bolt]

[vagrant nymph]

honestly its fine till now

[winter comet]

🫠

[vagrant nymph]

i dont understand what u told

[modest bolt]

Just expand sin x and leave that

[vagrant nymph]

alr bet

ill do that

ahh i dont think we are going anywhere after expanding sin x

like thats not helping

any other thing we can do?

[winter comet]

i meant expand cos(sin(x))

as a maclaurin series

with the taylor series formula

[vagrant nymph]

macalaurin seriess?

taylore series formula?

idk any of this

[winter comet]

have you seen this before?

[vagrant nymph]

nope

[winter comet]

bruh

[vagrant nymph]

we have not done much calcluas'

[winter comet]

so are you not supposed to use it then?

[vagrant nymph]

idtso

like the question is from my cocaching paper

sometimes they just give question out of syllabus

[winter comet]

they taught you just certain expansions but not the general formula for it ig? 🫠

[vagrant nymph]

yeaa

[vagrant nymph]

i think thell teach this later

[modest bolt]

You can still do it with cosx and sinx expansion

[vagrant nymph]

alr ill do it tmrw now

immgonna go sleep

[lyric cradle]

Why is the derivative of |sin x|-|cos x| discontinuous while the function itself is continuous?

[summer ruin]

continuity doesn't even imply the derivative exists at all

[hushed sphinx]

You don’t need the sine and cos to see this phenomenon -- |x| itself is a continuous function whose derivative has a undefined point with a jump discontinuity.

[high pelican]

that sucks

i mean it turns out most are nice but still

you should know e^x in general tho its an easy one

[river drift]

<@&268886789983436800>

[quasi pollen]

we love taylor series but they sometimes dont work (sometimes)

[alpine shore]

I need help on this guys.

[willow bear]

... integration is not really precalculus, and i specifically redirected you to #calculus, but fine.

ok.

@alpine shore

ok you moved.

[prisma aurora]

guys yall think i can do pre cal over the summer? like level of difficulty?

[final plaza]

I think it’s possible

[pastel lava]

Hello guys

Quick question

[willow bear]

well where is your question

[pseudo zealot]

i skipped into calc bc!!

[willow skiff]

congrats!!

[willow skiff]

go leaping, jumping, and galloping into calc BC my man

[tame pike]

Do I replace -4x with -3/x?

[uncut mulch]

no

to get
f(g(x)),
replace all x in f(x) = sqrt(2-4x)
with g(x), (or -3/x)

[tame pike]

Ok

[lime glade]

I hope this is a funny representation on how to compose functions

It also helps to write out the outside function while replacing the variables with parenthesis and then go back to write the second function in the empty parenthesis

[tame pike]

Ok, thanks 🙏

[modest bolt]

now I am imagining fog(gof(x)) with milk

[lime glade]

Theres other examples that uses sashimi and rice for sushi and my personal favorite is bread and eggs to make a sandwhich lmao

[spice nymph]

XD

oreo
rooe

oooo

re

f(x)=oo

g(x)=re

(f g)(x)=oreo

(g f)(x)=rooe

https://www.youtube.com/watch?v=sXxbkjlHvf4

literally functions.

[elfin jay]

XD not been even a week since started to study functions and got it

[spice nymph]

thats a GOOD way to see it

[vagrant nymph]

Is there any way to solve this without making like so many cases

[modest bolt]

Would you mind telling the answer?

To confirm what I did was right or wrong, I am not very sure about this.

[vagrant nymph]

20

[modest bolt]

I was very wrong lol

[vagrant nymph]

a is 1 b is 4 c is 3

[vagrant nymph]

It’s fine

[shell violet]

hello guys hw can i write that all element of a set are from a list ?

[willow skiff]

send the image pls

[shell violet]

already solve sry for the disruption

[willow skiff]

npnp

[hoary iris]

If you don't mind, How do you get the helpful role, south?

[willow skiff]

be active enough in help channels

[hoary iris]

I see, thank you!

[drifting oyster]

I'm very curious how did you come to this solution?

[willow skiff]

#help-43 message

I did a step-by-step here

it really helps, hearing from the person who was asking there

@vagrant nymph you'd probably appreciate a sol too

[drifting oyster]

I thought we were talking about the ceiling function and I was confused about the solution lol

[willow skiff]

ahhh

yeah the name 'greatest integer function'

it's shorthand for greatest integer that is less or equal to x

[drifting oyster]

Ah so basically floor x

[modest bolt]

I too did it [0,2) way and got wrong answer. Now I know the correct way

[vagrant nymph]

hmm yea makes a lot of sense

thankss @willow skiff

[silk ermine]

Guys

Geometry is betetr than calculus

[vagrant nymph]

r u telling or asking

[silk ermine]

İ am telling😱

[vagrant nymph]

yea ofc geomtry is beautiful💓

[silk ermine]

Yes bro 👏👏👏

[lyric cradle]

Does the integral of f(x) /dx signify something. How will such a integral be evaluated?

[drifting oyster]

[lyric cradle]

Geometry may be beautiful but it can't handle curves like calc

[vagrant nymph]

what is this question😭

[hushed sphinx]

You can either try to wing it by intuition, or actually compute the sets being compared.

[lime glade]

I'm more suprised i even still k ow how to read this
But alas i am too lazy to check each statement 🤣

[vagrant nymph]

i dont even understand it to wing it by intution🥲

like id ont get this part

[hushed sphinx]

Would you understand it better as $g(A) = { x \in \bR \mid f(x) \in A }$?

[obsidian monolith]

Troposphere

[vagrant nymph]

what does f(x)EA mean over here

like i understand the basic meaning

but we dont know what is A right

thiss is soo confusingg

[hushed sphinx]

The problem states that A is a subset of R.

So, a set of real numbers.

[vagrant nymph]

R is real numbers right?

yea okay

so basically g(x) is a set of some real numebrs?

[hushed sphinx]

I wouldn't write that, because that requires "x" to be a set of real numbers, which would be confusing.
The input to the function g is a set of real numbers. The output is also a (usually different) set of real numbers.

[vagrant nymph]

okay

makes more sense

leeme try this question again

okay i gfot it

thankks @hushed sphinx

[swift aurora]

bro someone teach me about differentiation of anything other than constants, e^x, 1/x and x

i want to learn integrals but i need to know diffs before i start grade 12

[hushed sphinx]

"Teach me everything about so-and-so" is a very big ask for a live chat. There are entire books written about what you want to know (usually with "calculus" in the title); get one of those and start working through it.

[swift aurora]

right
thats a good start

[empty otter]

search up product, quotient and power rule of differentiation on youtube

then do it for polynomials and rationals

then there's more that idk about

[whole void]

i agree. but did u know people were able to find the area from like 0 to pi of sin without calculus

[verbal geode]

Archimedes Polygon Method
Based on Equality right

[willow skiff]

method of exhaustion

[whole void]

No

[willow skiff]

https://math.stackexchange.com/questions/1931509/how-to-find-area-under-sines-without-calculus

ah I checked

sine as a function is definitely Renaissance era mathematics

but you don't even need to define sine as a function

[verbal geode]

I think "it is"
Archimedes Polygon Method through Inequality got an answer for finding Pi of sin

[willow skiff]

that's different

[whole void]

“pi of sin” ?

[verbal geode]

Sry
My phone screen makes me trouble

The Answer is Geomtric Reasoning
I think "it is"

[willow skiff]

that's just one specific type of geometric reasoning

you can't use the polygonal method on sine

[verbal geode]

Yes

But what are other types that can be solved without calculus for Finding area

[willow skiff]

parabolas, as per Archimedes

https://en.wikipedia.org/wiki/Method_of_exhaustion

there's this whole list

also Cavalieri's principle

https://en.wikipedia.org/wiki/Cavalieri's_principle#3-dimensional

[verbal geode]

Oh
That method also Suits to be correct for Archimedes Polygon principle as well
As you said Specific Type of Geomtric Reasoning

[willow skiff]

yes, the polygon is also geometric reasoning

[verbal geode]

Yup
It sounds correct rightv

[hoary iris]

Probably KA is good for beginners.

Is $\lim_{x \to 0}(1+kx)^{\frac1x}=e^k$?

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

I know that $\lim_{x \to \infty}\left(1+\frac{k}{x}\right)^{x}=e^k$

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

I see it is also true!

[hushed sphinx]

You need a one-sided limit where x approaches 0 from the right -- for small negative x, raising to the (1/x)th power is not well defined.

[hoary iris]

Is it only $\lim_{x \to 0^+}(1+kx)^{\frac1x}=e^k$ and not $\lim_{x \to 0^-}(1+kx)^{\frac1x}=e^k$?

[obsidian monolith]

Monkey•D•Luffy

[drifting oyster]

You run into some issues when approaching from the negative side...

Because 1/x will be negative

[modest bolt]

How did you make your background dark black? @hoary iris

[modest bolt]

Mine looks dull

[bleak mantle]

u mean gray

[hoary iris]

but grey is the best recommended for the general discord interface.

[slender notch]

Hello what do I do after this?

I modified a problem and now I do not know what to do haha

[raw hill]

It starts to telescope once n reaches 202

[slender notch]

So the answer is just 1/1005?

[slender notch]

Hi!
I'm confused...

[raw hill]

Tell me how you got 1/1005

[slender notch]

Misinterpretation

I interpreted it as telescoping before 202

oh okay

[raw hill]

u good now?

[slender notch]

Yep, the answer is ||1/1005 summation of 1/n||

Okay that did not make sense, hers an image

[raw hill]

👍

You can also write this using the harmonic numbers

$\frac{H_{201}}{1005}$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

where $H_n=\sum^{n}_{k=1} \frac{1}{k}$

[obsidian monolith]

Civil Service Pigeon

[slender notch]

NICE!!
THANK YOU!

[hoary iris]

Can we use any notational shorthand for limits like $L_{f(x)}=\lim_{x \to \infty}f(x)$ so that it means $L_{g(x)}=\lim_{x \to \infty}g(x)$ or $L_{f \circ g(x)}=\lim_{x \to \infty}f \circ g(x)$?

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

Can we do something like this? or is there any other representation there for it? <@&286206848099549185>

[modest bolt]

Let l(f(x)) = lim x→∞ f(x).
Then, l(g(x)) = lim x→∞ g(x),
l(fog(x)) = lim x→∞ fog(x).

Won't this work

There's no reason to introduce new notation but ofc you can do it for your convenience, but idk if teachers in exam consider it correct or not

[floral sigil]

its a 2 letter difference 😭

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

Ping me please if anyone has something to say to me for this!(Thank you!)

[hoary iris]

Not for the limit of f(x) = limit of g(x) but limit changing from e to 1

[hoary iris]

What is partial derivative?

[royal oracle]

do we actually learn that in precalc....

[winter comet]

a derivative with respect to one variable of a multivariable function, #multivariable-calculus

[hoary iris]

I see thank you xd

[river drift]

it's part of a total derivative :)

[winter comet]

for n=1, L_h(x) != e
but lim x->0 (1+x)^(1/x) = e, and lim x->inf (1+1/x)^x = e
which you can see when you replace x with 1/x and 0 with inf (so it all checks out)...

[winter comet]

you know i don't think i've ever thought about it like that

<@&268886789983436800> ?

almost pinged some guy called yamal

idk why @mode gave me yamal

[safe basin]

Now you gotta make yamal a mod whoever that is frfr

[long tapir]

Why is it 1?

They use squeeze theorem but i still dont understand how so

[winter comet]

sin(x) approximates x, and the error between them becomes 0 as x->0

[long tapir]

What im thinking is

Sin(0) = 0

x = 0

Shouldnt it be 0/0?

And therefore require us to do more math?

[winter comet]

yes

[long tapir]

But if you did squeeze theorem wouldnt you just get

-1/x <= sin(x)/x <= 1/x

[winter comet]

that doesn't really give you any new information though

since lim x->0 1/x or lim x->0 (-1/x) doesn't exist

[long tapir]

Yeah

Im just confused as to how to solve the problem

[winter comet]

did you see the solution by the squeeze theorem and not understand it?

[long tapir]

Did not

I just know it apparently uses squeeze theorem

[winter comet]

there are other ways like maclaurin series or l'hopital but :l

[winter comet]

oh

you want to find a function that you know is greater than sin(x)/x and one that is less than sin(x)/x right?

[river drift]

https://www.youtube.com/watch?v=5xitzTutKqM

[old bane]

How to find the range and domain of the natural log if there is an imaginary part (i) in it?

[river drift]

can you show the specific question you're working on?

[old bane]

ƒ(x)=sin{ln[5x^2 - 8x +4]}

[river drift]

so the logarithm is defined whenever the function inside is positive

[old bane]

its in iota

[river drift]

i assume you tried to solve 5x^2 - 8x + 4 = 0 and got a complex number solution

[old bane]

ya

[river drift]

but for our purposes, that means that the function is never equal to 0 in the real numbers

[old bane]

8+-4i / 10

[river drift]

so it's either always positive or always negative

[hoary iris]

Why is this happening?

[pliant bluff]

why are people using this channel for calculus :/

[hoary iris]

When people used this channel for calculus btw?

[pliant bluff]

ur literally using limits

and people were showing summation and stuff

literal integration aswell

[hushed sphinx]

I think it is because it is the only channel in the Pre-University category that has "calculus" in its name, and people who are learning calculus in high school may have a misconception that they're not supposed to use the Early University channels for their questions.

[pliant bluff]

ill be doing calculus for a levels in september but i alr know differentiation and some integration

basics ofc

school didnt teach us reciprocals of trig functions

or limits during pre calculus

[willow skiff]

they're going to teach you in A levels don't worry

[void charm]

Gamma function is the "only" to extended factorial function, but some conservative person think it is misdefined and they think there must be another function with different value. For example:
http://www.luschny.de/math/factorial/hadamard/HadamardsGammaFunction.html

[forest blaze]

in precalc manual you can find theese

[pliant bluff]

yayy

..

why the hell did i not get caught them in trig

at least i know sin csc cos sec tan cot

literally inversely named

or thats hwo i see it

so i can remember that, but anything to do with identities we havent actually started trying to learn

istg if my school skips anything important its gonna put everyone behind while im waiting

[void charm]

what about arcsin arccos arctan sinh cosh tanh?

[hoary iris]

Is it? I don't know limits is calculus! mb

[pliant bluff]

apparently its somehow pre calculus

[pliant bluff]

bro why would i know sinh and stuff

[hoary iris]

Is summation also in calculus?

[pliant bluff]

we only got caught the 3 basics

i dont see how hyperbolic functions matter in precalculus

pls explain bro

also arcsin and stuff can go away

i dont like the derivatives of them

[hoary iris]

why?

[pliant bluff]

i already know im not gonna like deriving with them

when i ever get there

the basic trig ones are easy, power easy, chain product quotient

ah yes, arc.

how about we get rid of those

and just use e^x

and lets change the world to base 6

[hoary iris]

trig is inevitable in our life lol

[pliant bluff]

roll of fake stream card scams

[noble lava]

see how you like integrating them

[pliant bluff]

i have no idea how that works :3

[noble lava]

Ignorance is bliss

[shrewd leaf]

yo yo yo i lust learned integration lol

[noble lava]

Nice

Did you like it?

Integration one of the most fun topics imo

[shrewd leaf]

yea its pretty cool, im just doing simple areas under graphs

[noble lava]

Ah

So definite indefinite are left

[shrewd leaf]

there alr but i cant do anything with them yet 🤷‍♂️

[noble lava]

O

[shrewd leaf]

got no idea how to use trig like sin and cos with integration lol

[noble lava]

It's fine dw

[willow skiff]

well integration is just the reverse of differentiation

[noble lava]

Concentrate on area under the curve first

[willow skiff]

so if d/dx (sin x) = cos x

you know the integral of cos x = sin x + c

[shrewd leaf]

fair enough if you know one you can get the other but im not sure how to get one in the first place lol

[shrewd leaf]

how would i find this lol

or is that crazy stuff

[willow skiff]

from first principles

so use the derivative definition, $\frac{d}{dx} \sin x = \lim_{h \to 0} \frac{\sin(x + h) - \sin(x)}{h}$

[obsidian monolith]

south

[willow skiff]

use the compound angle identity

[noble lava]

Have you been taught limits yet?

[willow skiff]

then there's these two famous limits, $\lim_{h \to 0} \frac{\sin h}{h}$ and $\lim_{h \to 0} \frac{\cos h - 1}{h}$

[obsidian monolith]

south

[shrewd leaf]

nah this is going straight over my head 😭

[willow skiff]

you need to go back to limits!!

[shrewd leaf]

yea havent been taught that yet ima take a look lol

[willow skiff]

we found the issue congrats

[noble lava]

Lol if you havent been taught it dont confuse yourself

If we use limits its just gonna be to find a differentiation

And after that its integration

So would just muddle 3 chaps up for ya

[shrewd leaf]

ah ty

[willow skiff]

yeah also get a proper textbook while you're at it

like Thomas's Calculus

[shrewd leaf]

that might help yea 😅

[willow skiff]

https://rodrigopacios.github.io/mrpacios/download/Thomas_Calculus.pdf

someone has a free copy here actually

[noble lava]

When you're at your peak

Like when you're done with 12th grade

I would suggest doing this

Uh

The peak of highschool math

[shrewd leaf]

ive not even started yet might take me a while lol

[willow skiff]

JEE only encourages shallow learning

[noble lava]

Yeah its ok the longer the better

[noble lava]

Mains yes

Advanced i wouldnt say so

[willow skiff]

oh I see

[noble lava]

Advanced is more in depth application

[willow skiff]

no then you might as well dive into linear algebra

[noble lava]

Mains is speed solving

[willow skiff]

might as well learn proper 1st year uni maths

[noble lava]

True

But just as a challenge i tried the calculus section

Of the book above

💀

Took me like a month to finish

[shrewd leaf]

jesus i kinda thought i was good at maths 😭 it feels like it never stops getting harder lol

[noble lava]

Same

Its beautiful tho

So i try to keep learning

Even if its not in syllabus

[sick fog]

I did this. Calculus in this book is chef's kiss

[hidden sun]

Anyone here did sheldon axler's precalculus

I'd be glad to know what book is the best continuation

[hoary iris]

@noble lava May I ask you a easy limit?(for fun)(If you're interested)

[noble lava]

Okay

[hoary iris]

,, \lim_{x \to 0}{\left(1+x^4\right)^{\frac{2}{x}}}

[noble lava]

1+x^4*(2-x)/x
2-x+2x^4-x^5/x
-1+8x^3-5x^4
=1/e

[hoary iris]

sorry its raised to the power of 2/x

[noble lava]

What

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

mb

[noble lava]

Oh wait

I did

A mistake

LMAO forgot formula

[hoary iris]

where?

[noble lava]

Its 1

[noble lava]

In this i used f*(g-1) instead of (f-1)*g

[hoary iris]

That's not a real problem lol

[noble lava]

No it was the same b4 too actually

[noble lava]

. This the ans

[hoary iris]

yeah!

[hexed yarrow]

! Help

[tender quest]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[noble lava]

This is not help

Its a challenge

[hoary iris]

to whom you're tell to?

us?

[hoary iris]

Is it? lol

[noble lava]

I mean thats what you said so yeah

[hoary iris]

Are you interested in giving me a limit?

[noble lava]

You just starting limits?

Or fairly proficient?

[hoary iris]

Yes on the pov of JEE

[noble lava]

O

[hoary iris]

[noble lava]

But youre done with all the 7 indeterminate forms?

[hoary iris]

Is there different techniques for each inderminate form?

[noble lava]

Yes

[hoary iris]

lol idk

Can you give me limit in the inderminate form except 0/0 0 * infinity?

Cause I haven't seen any limits other than these indeterminate form

[hoary iris]

If I am, Will I give this easy limit?

anyways Thank you for your time @noble lava !

[noble lava]

Try 6th

Just a simple one to test

[hoary iris]

0

[noble lava]

Correct

Did you do lhospital?

[hoary iris]

nope

[noble lava]

Small angle?

[hoary iris]

divide by 2x on num and den

[noble lava]

Oh good one, standard results

[hoary iris]

yeah

[noble lava]

This is my personal preference for this one

Fast af

[hoary iris]

what is small angle btw?

[noble lava]

Small angle approximation means that sin x when x approaches 0 can be written as x

[hoary iris]

oh my It's too good

[noble lava]

Indeed

[hoary iris]

I love that approach

[noble lava]

Same for tan x btw

[hoary iris]

but not for cosine lol

[noble lava]

But for cos x when x approaches 0 its 1

So even better lol

[hoary iris]

Where did you find those questions?

[noble lava]

15 is a better one, try it if you want

[noble lava]

That one was just from google but this one is from my coachings pdf

[hoary iris]

sure I will try now

[noble lava]

Former coachings*

[hoary iris]

0 by small angle?

[noble lava]

Yes but that wont work now

You can do that but it doesnt help you get closer

Since its 0/0

So indeterminate

[hoary iris]

well if it is 0/7x^4

[noble lava]

Dont forget x is 0 so you need to put that in the denom, and its small angle approximation, not an exact value

[noble lava]

Partial limit completion is a big no no

[hoary iris]

I see

[noble lava]

i.e. if u put x=0 in num you have to put it in denom

I'm sure you're finding this to be a pain in the ass by lhospital

[hoary iris]

yeah

[noble lava]

Try something else

Remember trigo

Large powers in the denom are generally a sign of using trigo formulae or series expansion

Ping when you have the answer or when you need a hint

[noble lava]

Though I'm a stubborn mule and would still do it by lhospital 💀 , but theres definitely easier ways

[hoary iris]

@noble lava hint please

[noble lava]

a^2-b^2= (a+b)(a-b)

[hoary iris]

@noble lava 🫠

[noble lava]

Did you use my hint

[hoary iris]

yes but I have no idea what to do after that😭

[noble lava]

Do you remember the formula for cos C- cos D

[hoary iris]

there is one such thing🤯

[noble lava]

Oh its not been taught to you?

[hoary iris]

yes it is but I didn't think of that

rn

[noble lava]

Ah

[hoary iris]

There is so much for me to learn!

[noble lava]

Always

The learning must never stop

Unless you're on vacation

In which case

It can

[hoary iris]

I haven't even thought of single step to this limit

[noble lava]

Well you still know the lhospital way

[hoary iris]

so both the l hop and the differnet method are of same time to execute?

[noble lava]

Also this was sent by my instructor when we finished limits

Like one month b4 the end of grade 11 so we had almost finished determinants by then

[hoary iris]

According to you, what is it's level?

[noble lava]

Oh nah

[noble lava]

12*

Not 11 💀

[hoary iris]

What is this limit's level?

[noble lava]

Uh on a scale of 1 to 10 from all the problems you're going to see, a 7

(For jee)